First, the Roth account in your 403(b) was not a Roth IRA.
Second, a distribution reported with code H is never taxable. A From 1099-R with code H in box 7 is always to have a zero in box 2a and box 2b Taxable amount not determined unmarked, so the 403(b) plan prepared the Form 1099-R incorrectly. To accommodate such erroneous Forms 1099-R, it would probably be better if TurboTax always automatically treated code H as meaning nontaxable, but that's unlikely to ever happen.
It's doubtful that the 403(b) plan will admit their error, so just enter a zero in box 2a of TurboTax's 1099-R form. The fact that you have done so will not be apparent to the IRS.
